1. Field of the Invention
The present invention relates to a method of driving liquid crystals and a display apparatus therefor, and in particular to a driving method of displaying STN (Super Twisted Nematic) liquid crystals with high contrast and a display apparatus therefor.
2. Description of the Related Art
As a conventional driving method of a liquid crystal display apparatus having a matrix structure, there is known a technique described in xe2x80x9cUltimate Limits for Matrix Addressing of RMS-Responding Liquid-Crystal Displays,xe2x80x9d IEEE Transactions on Electron Devices, Vol. ED-26, No. 5, May 1979 (pp. 795-802) and xe2x80x9cActive Addressing Method for High-Contrast Video-Rate STN Displays,xe2x80x9d SID 92 DIGEST, pp. 228-231. According to this technique, each row electrode is provided with a voltage depending upon an orthogonal function, whereas each column electrode is provided with a voltage depending upon a function obtained as a sum of products of every display information of that column and a function of the scanning side. The driving method will hereafter be described in detail by referring to FIGS. 1 to 4.
FIG. 1 shows the structure of a liquid crystal display panel having a matrix structure consisting of N rows by M columns. An intersection of a row electrode and a column electrode forms a dot D(i,j). A voltage represented by a function f(i) (i=1, 2, . . . N) is supplied to each of the N row electrodes. A voltage represented by a function g(j) (j=1, 2, . . . M) is supplied to each of the M column electrodes. U(i,j) denotes a voltage supplied to the dot D(i,j). The voltage U(i,j) is a difference between values of the voltage functions f(i) and g(j). In the ensuing description, voltage is normalized. FIG. 2 is a diagram showing an example of orthogonal function voltages supplied to row electrodes to drive STN liquid crystal displays. This example is generally used at the present time. Assuming now that the function f(i) is represented by FIG. 2, the functions f(i) and g(j) can be represented by equations (1) and (2), respectively.
f(i)=FPxc2x7xcex4(i,t)xe2x80x83xe2x80x83(1) 
                              g          ⁡                      (            j            )                          =                              1                          N                                ⁢                      xe2x80x83                    ⁢                                    ∑                              i                =                1                            N                        ⁢                          xe2x80x83                        ⁢                                          P                ⁡                                  (                                      i                    ,                    j                                    )                                            ⁢                              f                ⁡                                  (                  i                  )                                                                                        (        2        )            
In the equations (1) and (2), xcex4(i,t) is 1 for i=t and 0 for ixe2x89xa0t. FP is a constant given by the following equation (3).                     FP        =                                            N              ⁢                              N                                                    2              ⁢                              (                                                      N                                    -                  1                                )                                                                        (        3        )            
P(i,j) denotes display information of the dot D(i,j). P(i,j) is xe2x88x921 for a display-on state and 1 for a display-off state. By using equations (1), (2) and (3), the effective voltage Urms(i,j) applied to the dot D(i,j) at this time can be represented by the following equation (4).                                                                                           U                  rms                                ⁡                                  (                                      i                    ,                    j                                    )                                            =                              xe2x80x83                            ⁢              A2                                                                          =                              xe2x80x83                            ⁢                                                [                                                                                    1                        T                                            ⁢                                                                        ∫                          0                          T                                                ⁢                                                                                                            f                              ⁡                                                              (                                i                                )                                                                                      2                                                    ⁢                                                      xe2x80x83                                                    ⁢                                                      ⅆ                            t                                                                                                                +                                                                  1                        T                                            ⁢                                                                        ∫                          0                          T                                                ⁢                                                                                                            g                              ⁡                                                              (                                j                                )                                                                                      2                                                    ⁢                                                      2                            T                                                    ⁢                                                                                    ∫                              0                              T                                                        ⁢                                                                                          f                                ⁡                                                                  (                                  i                                  )                                                                                            ⁢                                                              g                                ⁡                                                                  (                                  j                                  )                                                                                            ⁢                                                              xe2x80x83                                                            ⁢                                                              ⅆ                                t                                                                                                                                                                                          ]                                                  1                  /                  2                                                                                        (        4        )            
Letting T=N and rewriting (4) gives                                           1            T                    ⁢                                    ∫              0              T                        ⁢                                                            f                  ⁡                                      (                    i                    )                                                  2                            ⁢                              xe2x80x83                            ⁢                              ⅆ                t                                                    =                                            1              N                        ⁢                                          ∑                                  t                  =                  1                                N                            ⁢                              xe2x80x83                            ⁢                                                (                                                            FP                      ·                      δ                                        ⁢                                          xe2x80x83                                        ⁢                                          (                                              i                        ,                        t                                            )                                                        )                                2                                              =                                    N                                      2              ⁢                              (                                                      N                                    -                  1                                )                                                                        (        5        )                                                      1            T                    ⁢                                    ∫              0              T                        ⁢                                          g                ⁡                                  (                  j                  )                                            2                                      =                                            1              N                        ⁢                                          ∑                                  t                  =                  1                                N                            ⁢                              xe2x80x83                            ⁢                                                (                                                            1                                              N                                                              ⁢                                          xe2x80x83                                        ⁢                                                                  ∑                                                  i                          =                          1                                                N                                            ⁢                                              xe2x80x83                                            ⁢                                                                        P                          ⁡                                                      (                                                          i                              ,                              j                                                        )                                                                          ⁢                                                  f                          ⁡                                                      (                            i                            )                                                                                                                                )                                2                                              =                                                    1                N                            ⁢                                                ∑                                      t                    =                    1                                    N                                ⁢                                                      [                                                                  1                                                  N                                                                    ⁢                                                                        ∑                                                      i                            =                            1                                                    N                                                ⁢                                                  xe2x80x83                                                ⁢                                                                              P                            ⁡                                                          (                                                              i                                ,                                j                                                            )                                                                                ⁢                                                                                                                                                      N                                  ⁢                                                                      N                                                                                                                                    2                                  ⁢                                                                      (                                                                                                                  N                                                                            -                                      1                                                                        )                                                                                                                                                        ·                            δ                                                    ⁢                                                      xe2x80x83                                                    ⁢                                                      (                                                          i                              ,                              t                                                        )                                                                                                                ]                                    2                                                      =                                                                                1                    N                                    ·                                      1                    N                                    ·                                                            N                      ⁢                                              N                                                                                    2                      ⁢                                              (                                                                              N                                                    -                          1                                                )                                                                                            ⁢                                                      ∑                                          t                      =                      1                                        N                                    ⁢                                      xe2x80x83                                    ⁢                                                            [                                                                        ∑                                                      t                            =                            1                                                    N                                                ⁢                                                  xe2x80x83                                                ⁢                                                                              P                            ⁡                                                          (                                                              i                                ,                                j                                                            )                                                                                ⁢                                                      xe2x80x83                                                    ⁢                          δ                          ⁢                                                      xe2x80x83                                                    ⁢                                                      (                                                          i                              ,                              t                                                        )                                                                                              ]                                        2                                                              =                                                                    1                    N                                    ⁢                                      xe2x80x83                                    ⁢                                                                                    N                                                                    2                        ⁢                                                  (                                                                                    N                                                        -                            1                                                    )                                                                                      ·                    N                                                  =                                                      N                                                        2                    ⁢                                          (                                                                        N                                                -                        1                                            )                                                                                                                              (        6        )                                                      2            T                    ⁢                                    ∫              0              T                        ⁢                                          f                ⁡                                  (                  i                  )                                            ⁢                              g                ⁡                                  (                  j                  )                                            ⁢                              xe2x80x83                            ⁢                              ⅆ                t                                                    =                                            2              N                        ⁢                                          ∑                                  t                  =                  1                                N                            ⁢                              xe2x80x83                            ⁢                                                f                  ⁡                                      (                    i                    )                                                  ⁢                                                      ∑                                          i                      =                      1                                        N                                    ⁢                                      xe2x80x83                                    ⁢                                                            1                                              N                                                              ⁢                                          P                      ⁡                                              (                                                  i                          ,                          j                                                )                                                              ⁢                                          f                      ⁡                                              (                        i                        )                                                                                                                          =                                    2              N                        ⁢                                          ∑                                  t                  =                  1                                N                            ⁢                              xe2x80x83                            ⁢                                                                                          N                      ⁢                                              N                                                                                    2                      ⁢                                              (                                                                              N                                                    -                          1                                                )                                                                                            ·                                  "AutoLeftMatch"                                                            δ                      ⁢                                              xe2x80x83                                            ⁢                                              (                                                  i                          ,                          t                                                )                                            ⁢                                              xe2x80x83                                            ⁢                                                                        ∑                                                      i                            =                            1                                                    N                                                ⁢                                                  xe2x80x83                                                ⁢                                                                              1                                                          N                                                                                ⁢                                                      xe2x80x83                                                    ⁢                                                      P                            ⁡                                                          (                                                              i                                ,                                j                                                            )                                                                                ⁢                                                                                                                                                      N                                  ⁢                                                                      N                                                                                                                                    2                                  ⁢                                                                      (                                                                                                                  N                                                                            -                                      1                                                                        )                                                                                                                                                        ·                            δ                                                    ⁢                                                      xe2x80x83                                                    ⁢                                                      (                                                          i                              ,                              t                                                        )                                                                                                                =                                                                                            2                                                      N                            ⁢                                                          N                                                                                                      ·                                                                              N                            ⁢                                                          N                                                                                                            2                            ⁢                                                          (                                                                                                N                                                                -                                1                                                            )                                                                                                      ·                                                                              ∑                                                          t                              =                              1                                                        N                                                    ⁢                                                      xe2x80x83                                                    ⁢                                                      δ                            ⁢                                                          xe2x80x83                                                        ⁢                                                          (                                                              i                                ,                                t                                                            )                                                        ⁢                                                                                          ∑                                                                  i                                  =                                  1                                                                N                                                            ⁢                                                              xe2x80x83                                                            ⁢                                                                                                P                                  ⁡                                                                      (                                                                          i                                      ,                                      j                                                                        )                                                                                                  ⁢                                                                  xe2x80x83                                                                ⁢                                δ                                ⁢                                                                  xe2x80x83                                                                ⁢                                                                  (                                                                      i                                    ,                                    t                                                                    )                                                                                                                                                                                        =                                                                        2                                                      2                            ⁢                                                          (                                                                                                N                                                                -                                1                                                            )                                                                                                      ·                                                  P                          ⁡                                                      (                                                          i                              ,                              j                                                        )                                                                                                                                                                                                      (        7        )            
From equations (5), (6) and (7), therefore, the effective voltage Urms(i,j) can be written as                                                                                           U                  rms                                ⁡                                  (                                      i                    ,                    j                                    )                                            =                              xe2x80x83                            ⁢                                                [                                                                                    N                                                                    2                        ⁢                                                  (                                                                                    N                                                        -                            1                                                    )                                                                                      +                                                                  N                                                                    2                        ⁢                                                  (                                                                                    N                                                        -                            1                                                    )                                                                                      -                                                                  2                                                  2                          ⁢                                                      (                                                                                          N                                                            -                              1                                                        )                                                                                              ⁢                                              xe2x80x83                                            ⁢                                              P                        ⁡                                                  (                                                      i                            ,                            j                                                    )                                                                                                      ]                                                  1                  /                  2                                                                                                        =                              xe2x80x83                            ⁢                                                [                                                                                    2                        ⁢                                                  N                                                                                            2                        ⁢                                                  (                                                                                    N                                                        -                            1                                                    )                                                                                      -                                                                  2                        ⁢                                                  P                          ⁡                                                      (                                                          i                              ,                              j                                                        )                                                                                                                      2                        ⁢                                                  (                                                                                    N                                                        -                            1                                                    )                                                                                                      ]                                                  1                  /                  2                                                                                        (        8        )            
Assuming that the dot D(i,j) is in the display-on state, P(i,j)=xe2x88x921 and the effective voltage Urms(i,j) is represented by equation (9). Assuming that the dot D(i,j) is in the display-off state, P(i,j)=1 and the effective voltage Urms(i,j) is represented by equation (10).                                           U            rms                    ⁡                      (                          i              ,              j                        )                          =                                            [                                                                    2                    ⁢                                          N                                                                            2                    ⁢                                          (                                                                        N                                                -                        1                                            )                                                                      -                                                      -                    2                                                        2                    ⁢                                          (                                                                        N                                                -                        1                                            )                                                                                  ]                                      1              2                                =                                    [                                                                    N                                    +                  1                                                                      N                                    -                  1                                            ]                                      1              2                                                          (        9        )                                                      U            rms                    ⁡                      (                          i              ,              j                        )                          =                                            [                                                                    2                    ⁢                                          N                                                                            2                    ⁢                                          (                                                                        N                                                -                        1                                            )                                                                      -                                  2                                      2                    ⁢                                          (                                                                        N                                                -                        1                                            )                                                                                  ]                                      1              2                                =          1                                    (        10        )            
The voltage applied to the dot D(i,j) is (f(i)xe2x88x92g(j)) and has a waveform as shown in FIG. 3 on the basis of equations (1) and (2). In FIG. 3, S1, S2 and S3 are represented by the following equations.       S1    =                                                                                        N                  ⁢                                      N                                                                    2                  ⁢                                      (                                                                  N                                            -                      1                                        )                                                                        +                                                            N                                                  2                  ⁢                                      (                                                                  N                                            -                      1                                        )                                                                                                            (            11            )                                                            (                                          When                ⁢                                  xe2x80x83                                ⁢                                  D                  ⁡                                      (                                          i                      ,                      j                                        )                                                              =                              display                ⁢                                  xe2x80x83                                ⁢                on                                      )                                                xe2x80x83                                                                                                                                N                    ⁢                                          N                                                                            2                    ⁢                                          (                                                                        N                                                -                        1                                            )                                                                                  -                                                                    N                                                        2                    ⁢                                          (                                                                        N                                                -                        1                                            )                                                                                            ⁢                          xe2x80x83                                                            (            12            )                                                                          (                                                When                  ⁢                                      xe2x80x83                                    ⁢                                      D                    ⁡                                          (                                              i                        ,                        j                                            )                                                                      =                                  display                  ⁢                                      xe2x80x83                                    ⁢                  off                                            )                        ⁢                          xe2x80x83                                                            xe2x80x83                                                                        S2            =                                                            N                                                  2                  ⁢                                      (                                                                  N                                            -                      1                                        )                                                                                ⁢                      xe2x80x83                                                (          13          )                                              S3          =                      -                                                            N                                                  2                  ⁢                                      (                                                                  N                                            -                      1                                        )                                                                                                            (          14          )                    
Assuming now that N=240, we get S1=12.1 (when D(i,j)=display on), S1=10.6 (when D(i,j)=display off), S2=0.73, and S3=xe2x88x920.73. As a result, a large voltage is applied once (i=t) during one frame (i.e., a period of t=1 to N) and a low voltage is applied during the remaining intervals. In fast responding STN liquid crystal displays, the display luminance lowers while this low voltage is being applied.
As a driving method for avoiding this, a method described below has been proposed. FIG. 4 shows orthogonal functions called Walsh functions. In the example shown in FIG. 4, the number of divisions (time intervals) of the Walsh functions is 8. Assuming now that Walsh functions with the number of divisions being equivalent to T are used as the function f(i) of the voltage applied to row electrodes of the liquid crystal display panel of FIG. 1 and N Walsh functions are selected out of T Walsh functions (Txe2x89xa7N) and used as the function f(i), the effective voltage value Urms(i,j) of the dot D(i,j) will be is derived.
It is assumed that the functions f(i) and g(j) are represented by the following equations (15) and (16).
f(i)=FPxc2x7W(i,t)xe2x80x83xe2x80x83(15) 
                              g          ⁡                      (            j            )                          =                              1                          N                                ⁢                      xe2x80x83                    ⁢                                    ∑                              i                =                1                            N                        ⁢                          xe2x80x83                        ⁢                                          P                ⁡                                  (                                      i                    ,                    j                                    )                                            ⁢                              f                ⁡                                  (                  i                  )                                                                                        (        16        )            
In these equations, W(i,t) is a Walsh function and has a value of 1 or 31 1. FP is a constant indicated by equation (17).                     FP        =                                            N                                      2              ⁢                              (                                                      N                                    -                  1                                )                                                                        (        17        )            
In equation (4),                                                                                           1                  T                                ⁢                                                      ∫                    0                    T                                    ⁢                                                                                    f                        ⁡                                                  (                          i                          )                                                                    2                                        ⁢                                          xe2x80x83                                        ⁢                                          ⅆ                      t                                                                                  =                              xe2x80x83                            ⁢                                                1                  T                                ⁢                                  xe2x80x83                                ⁢                                                      ∑                                          t                      =                      1                                        T                                    ⁢                                      xe2x80x83                                    ⁢                                                            (                                              FP                        ·                                                  W                          ⁡                                                      (                                                          i                              ,                              t                                                        )                                                                                              )                                        2                                                                                                                          =                              xe2x80x83                            ⁢                                                1                  T                                ⁢                                  {                                                                                    FP                        2                                            ⁢                                                                        W                          ⁡                                                      (                                                          i                              ,                              1                                                        )                                                                          2                                                              +                                                                  FP                        2                                            ⁢                                                                        W                          ⁡                                                      (                                                          i                              ,                              2                                                        )                                                                          2                                                              +                    …                    +                                                                  FP                        2                                            ⁢                                                                        W                          ⁡                                                      (                                                          i                              ,                              T                                                        )                                                                          2                                                                              }                                                                                                        =                              xe2x80x83                            ⁢                                                                    1                    T                                    ·                                      FP                    2                                    ·                                                            T                      ⁡                                              (                                                  ±                          1                                                )                                                              2                                                  =                                                      FP                    2                                    =                                                            N                                                              2                      ⁢                                              (                                                                              N                                                    -                          1                                                )                                                                                                                                                    (        18        )                                                                                                      1                  T                                ⁢                                                      ∫                    0                    T                                    ⁢                                                                                    g                        ⁡                                                  (                          j                          )                                                                    2                                        ⁢                                          xe2x80x83                                        ⁢                                          ⅆ                      t                                                                                  =                              xe2x80x83                            ⁢                                                1                  T                                ⁢                                                      ∑                                          t                      =                      1                                        T                                    ⁢                                                            (                                                                        1                                                      N                                                                          ⁢                                                                              ∑                                                          i                              =                              1                                                        N                                                    ⁢                                                      xe2x80x83                                                    ⁢                                                                                                                    P                                ⁡                                                                  (                                                                      i                                    ,                                    j                                                                    )                                                                                            ·                                                                                                                                    N                                                                                                        2                                    ⁢                                                                          (                                                                                                                        N                                                                                -                                        1                                                                            )                                                                                                                                                                                            ⁢                                                          W                              ⁡                                                              (                                                                  i                                  ,                                  t                                                                )                                                                                                                                                        )                                        2                                                                                                                          =                              xe2x80x83                            ⁢                                                                    1                    T                                    ·                                      1                    N                                    ·                                                            N                                                              2                      ⁢                                              (                                                                              N                                                    -                          1                                                )                                                                                            ⁢                                                                            xe2x80x83                                        ∑                                                        t                    =                    1                                    T                                ⁢                                                      ∑                                          i                      =                      1                                        N                                    ⁢                                                            (                                                                        P                          ⁡                                                      (                                                          i                              ,                              j                                                        )                                                                          ·                                                  W                          ⁡                                                      (                                                          i                              ,                              t                                                        )                                                                                              )                                        2                                                                                                                          =                              xe2x80x83                            ⁢                                                                    1                    T                                    ·                                      1                    N                                    ·                                                            N                                                              2                      ⁢                                              (                                                                              N                                                    -                          1                                                )                                                                                            ⁢                                  xe2x80x83                                ⁢                                                      ∑                                          t                      =                      1                                        T                                    ⁢                                      {                                                                                                                        P                            ⁡                                                          (                                                              1                                ,                                j                                                            )                                                                                2                                                ⁢                                                                              W                            ⁡                                                          (                                                              1                                ,                                t                                                            )                                                                                2                                                                    +                      …                      +                                                                                                                                                              xe2x80x83                            ⁢                                                                                          P                      ⁡                                              (                                                  N                          ,                          j                                                )                                                              2                                    ⁢                                                            W                      ⁡                                              (                                                  N                          ,                          t                                                )                                                              2                                                  }                                                                                        =                              xe2x80x83                            ⁢                                                                                          1                      T                                        ·                                          1                      N                                                        ⁢                                      xe2x80x83                                    ⁢                                                                                    N                                                                    2                        ⁢                                                  (                                                                                    N                                                        -                            1                                                    )                                                                                      ·                    T                    ·                    N                                                  =                                                      N                                                        2                    ⁢                                          (                                                                        N                                                -                        1                                            )                                                                                                                              (        19        )                                                                                                      2                  T                                ⁢                                                      ∫                    0                    T                                    ⁢                                                            f                      ⁡                                              (                        i                        )                                                              ⁢                                          g                      ⁡                                              (                        j                        )                                                              ⁢                                          xe2x80x83                                        ⁢                                          ⅆ                      t                                                                                  =                              xe2x80x83                            ⁢                                                2                  T                                ⁢                                                      ∑                                          t                      =                      1                                        T                                    ⁢                                      xe2x80x83                                    ⁢                                                            FP                      ·                                              W                        ⁡                                                  (                                                      i                            ,                            t                                                    )                                                                                      ⁢                                                                  ∑                                                  i                          =                          1                                                N                                            ⁢                                                                        1                                                      N                                                                          ⁢                                                  xe2x80x83                                                ⁢                                                  P                          ⁡                                                      (                                                          i                              ,                              j                                                        )                                                                          ⁢                                                  FP                          ·                                                      W                            ⁡                                                          (                                                              i                                ,                                t                                                            )                                                                                                                                                                                                                                                  =                              xe2x80x83                            ⁢                                                                    2                    T                                    ·                                      1                                          N                                                        ·                                                            N                                                              2                      ⁢                                              (                                                                              N                                                    -                          1                                                )                                                                                            ⁢                                                                            xe2x80x83                                        ∑                                                        t                    =                    1                                    T                                ⁢                                  W                  ⁡                                      (                                          i                      ,                      t                                        )                                                  ⁢                                                      ∑                                          i                      =                      1                                        N                                    ⁢                                                            P                      ⁡                                              (                                                  i                          ,                          j                                                )                                                              ⁢                                          W                      ⁡                                              (                                                  i                          ,                          t                                                )                                                                                                                                                                    =                              xe2x80x83                            ⁢                                                                    2                    T                                    ·                                      1                                          2                      ⁢                                              (                                                                              N                                                    -                          1                                                )                                                                                            ⁢                                                                            xe2x80x83                                        ∑                                                        t                    =                    1                                    T                                ⁢                                  P                  ⁡                                      (                                          i                      ,                      j                                        )                                                  ⁢                                                      W                    ⁡                                          (                                              i                        ,                        t                                            )                                                        2                                                                                                        =                              xe2x80x83                            ⁢                                                2                  ⁢                                      P                    ⁡                                          (                                              i                        ,                        j                                            )                                                                                        2                  ⁢                                      (                                                                  N                                            -                      1                                        )                                                                                                          (        20        )            
The effective voltage Urms(i,j) of the dot D(i,j) becomes                                                                                           U                  rms                                ⁡                                  (                                      i                    ,                    j                                    )                                            =                              xe2x80x83                            ⁢                                                [                                                                                    N                                                                    2                        ⁢                                                  (                                                                                    N                                                        -                            1                                                    )                                                                                      +                                                                  N                                                                    2                        ⁢                                                  (                                                                                    N                                                        -                            1                                                    )                                                                                      -                                                                  2                        ⁢                                                  P                          ⁡                                                      (                                                          i                              ,                              j                                                        )                                                                                                                      2                        ⁢                                                  (                                                                                    N                                                        -                            1                                                    )                                                                                                      ]                                                  1                  2                                                                                                        =                              xe2x80x83                            ⁢                                                [                                                                                    2                        ⁢                                                  N                                                                                            2                        ⁢                                                  (                                                                                    N                                                        -                            1                                                    )                                                                                      -                                                                  2                        ⁢                                                  P                          ⁡                                                      (                                                          i                              ,                              j                                                        )                                                                                                                      2                        ⁢                                                  (                                                                                    N                                                        -                            1                                                    )                                                                                                      ]                                                  1                  2                                                                                        (        21        )            
As evident from the results heretofore described, the effective voltage Urms(i,j) obtained when the Walsh function is used becomes identical with equation (8). Urms(i,j) has a value of equation (9) for the display-on state, whereas Urms(i,j) has a value of equation (10) for the display-off state.
In this case, g(j) of equation (16) is rewritten as                                                                         g                ⁡                                  (                  j                  )                                            =                              xe2x80x83                            ⁢                                                1                                      N                                                  ⁢                                                      ∑                                          i                      =                      j                                        N                                    ⁢                                      xe2x80x83                                    ⁢                                                            P                      ⁡                                              (                                                  i                          ,                          j                                                )                                                              ⁢                                          f                      ⁡                                              (                        i                        )                                                                                                                                                                    =                              xe2x80x83                            ⁢                                                FP                                      N                                                  ⁢                                  xe2x80x83                                ⁢                                  (                                                            2                      ⁢                      D                                        -                    N                                    )                                                                                        (        22        )            
where D is the number of coincident values of P(i,j) with respect to W(i,t) with i=1 to N in the j-th column (P(i,j) assumes a value of xc2x11, and W(i,t) assumes a value of xc2x11). At this time, the value of D has a normal distribution represented by the following equation.                               P          ⁡                      (            D            )                          ≃                                            2                              π                ⁢                                  xe2x80x83                                ⁢                N                                              ⁢                      xe2x80x83                    ⁢                      exp            ⁢                          xe2x80x83                        [                                          -                                                      (                                                                  2                        ⁢                        D                                            -                      N                                        )                                    2                                                            2                ⁢                N                                      ]                                              (        23        )            
As indicated by equation (23), D has a normal distribution around N/2. Therefore, equation (22) also has a normal distribution in the same way. As compared with FIG. 3, therefore, the average voltage over the period of t=1 to N is applied to the dot D(i,j) as the voltage waveform (f(i)xe2x88x92g(j)).
D can assume a value ranging from 0 (complete noncoincidence) to N (entire coincidence). From equation (22), the peak value of g(j) becomes                                                                                           g                  ⁡                                      (                    j                    )                                                                    P                  -                  P                                            =                                                FP                                      N                                                  ⁢                                  (                                      ±                    N                                    )                                                                                                        =                                                ±                                      N                                                  ⁢                FP                                                                        (                  23          xe2x80x2                )            
Furthermore, g(j) can have any one of N+1 levels. Regarding this liquid crystal display device as a display device for a personal computer, N=240 rows are needed. As the column voltage g(j), therefore, a liquid crystal driver generating 241 levels and generating a peak voltage of approximately 22.65 volts (in case the nonselection voltage of the liquid crystal display is 1 volt) on the basis of equation (23) is needed. Since it is difficult to realize such a liquid crystal driver, it is said that the liquid crystal driver having 64 levels (where the peak voltage is 5.95 volts) is sufficient on the basis of the property of D having a normal distribution. In this case, however, overflow, i.e., a voltage exceeding 64 levels, might be needed with a probability of once every 115 frames. However, it is said that overflow occurs very rarely in an actual display and hence there is no problem in the above described conventional technique.
If a Walsh function is used as the voltage function supplied to the row electrodes in the above described driving method, however, the voltage function g(j) supplied to the column electrodes becomes as represented by the following equation (24) on the basis of equations (15) and (16). For determining the voltage applied to one dot at a certain time t, it is necessary to calculate the sum of products of the display information P(i,j) for i=1 to N and the Walsh function W(i,t). The implementation of this is difficult, and a specific driving circuit for doing so has not been clearly described                                                                         g                ⁡                                  (                  j                  )                                            =                                                1                                      N                                                  ⁢                                                      ∑                                          i                      =                      1                                        N                                    ⁢                                      xe2x80x83                                    ⁢                                                            P                      ⁡                                              (                                                  i                          ,                          j                                                )                                                              ⁢                                          FP                      ·                                              W                        ⁡                                                  (                                                      i                            ,                            t                                                    )                                                                                                                                                                                            =                                                FP                                      N                                                  ⁢                                                      ∑                                          i                      =                      1                                        N                                    ⁢                                      xe2x80x83                                    ⁢                                                            P                      ⁡                                              (                                                  i                          ,                          j                                                )                                                              ⁢                                          W                      ⁡                                              (                                                  i                          ,                          t                                                )                                                                                                                                                    (        24        )            
Assuming that the voltage function supplied to the row electrodes is the function shown in FIG. 2, the voltage function g(j) applied to the column electrodes is represented by the following equation (25).                                                                         g                ⁡                                  (                  j                  )                                            =                                                1                                      N                                                  ⁢                                                      ∑                                          i                      =                      1                                        N                                    ⁢                                      xe2x80x83                                    ⁢                                                            P                      ⁡                                              (                                                  i                          ,                          j                                                )                                                              ⁢                                          FP                      ·                      δ                                        ⁢                                          xe2x80x83                                        ⁢                                          (                                              i                        ,                        t                                            )                                                                                                                                              =                                                FP                                      N                                                  ⁢                                                      ∑                                          i                      =                      1                                        N                                    ⁢                                      xe2x80x83                                    ⁢                                                            P                      ⁡                                              (                                                  i                          ,                          j                                                )                                                              ⁢                                          xe2x80x83                                        ⁢                    δ                    ⁢                                          xe2x80x83                                        ⁢                                          (                                              i                        ,                        t                                            )                                                                                                                                              =                                                FP                                      N                                                  ⁢                                  P                  ⁡                                      (                                          i                      ,                      j                                        )                                                                                                          (        25        )            
The product summation thus becomes unnecessary and the circuit configuration becomes simple. In this case, however, the voltage waveform applied to the dot D(i,j) assumes a high voltage during only one interval in N intervals, and assumes a low voltage during the remaining Nxe2x88x921 intervals. In the case of fast responding STN liquid crystal displays, therefore, the contrast drops.
Furthermore, in the conventional technique, a liquid crystal driver generating the column voltage is required to provide N+1 levels and the peak voltage expressed by equation (23). However, it is said that a liquid crystal driver having 64 levels and approximately 5.95 volts suffices for a personal computer display having N=240, considering the property of the value assumed by D. Therefore, overflow occurs with a probability of once every 115 frames. In this case, it is considered that overflow occurs with a probability defined by the normal distribution following the above described theory when the contents of display change momentarily as in a moving picture display. In displays used for information processing devices such as personal computers or work stations, however, contents of displays are not always moving pictures but are still pictures in many cases. If overflow occurs once in a still picture, therefore, overflow occurs in every frame and D loses its property of having a normal distribution. Therefore, the effective value of the pertinent column electrode voltage decreases and the quality of the display is degraded.
An object of the present invention is to provide a circuit which has a simple circuit configuration and which does not degrade contrast for fast responding STN liquid crystal displays.
Another object of the present invention is to provide a new liquid crystal driving method which can also be applied to displays of still pictures in personal computers or the like using fast responding STN liquid crystal displays.
In order to achieve the above described objects, a display apparatus includes a row function generation circuit, a function generation circuit, a line memory for storing display data of X rows, a computation circuit for performing computation based on the output of the function generation circuit, and a voltage conversion circuit for converting the output of the computation circuit to a voltage.
The row function generation circuit generates a function for N rows so that only X rows out of the N rows are Walsh functions at a certain time t and the remaining rows are 0. The row function generation circuit supplies the function thus generated to a row electrode driver of the liquid crystal display. The function generation circuit generates values identical with values of the above described Walsh functions of X rows. The outputs are subjected to computation together with the output of the line memory. The result of the computation is converted into voltage, which is supplied to the column electrode drive.